The federation, also known as the FAI, said Baumgartner notched up the world's maximum vertical speed record, as well as the highest exit altitude and vertical distance of freefall.
The FAI confirmed a final analysis by Baumgartner's team Red Bull Stratos, which said that the 43-year-old reached 1,357.6 kilometres (843.6 miles) an hour, or Mach 1.25, in freefall.
Baumgartner's jump took place last October 14 in Roswell in the US state of New Mexico.
He was first carried up in a pressurised capsule attached to a helium balloon to an altitude of 38,969.4 metres (127,852.4 feet).
Wearing a specially-designed survival suit, he launched himself to Earth, freefalling 36,402.6 metres before opening his parachute.
"By breaking these world records, Felix adds his names to the list of FAI world record holders which includes prestigious air sport personalities such as Charles Lindbergh, Yuri Gagarin and, more recently, Bertrand Piccard and Steve Fossett," the federation underlined.